8.If `(u+1/u) = 8` then find the value of `u^2+1/u^2`

If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2 , then find the value of f^(prime)(1) .

If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2 , then find the value of f^(prime)(1) .

If u+t=5 and u-t=2 , what is the value of (u-t)(u^2-t^2) ?

If U_n=int_0^(pi/2)(sin^2n x)/(sin^2x)dx, then show that U_1,U_2,U_3.......U_n constitute an AP. Hence or otherwise find the value of U_n.

If u=sin^(-1)((2x)/(1+x^2)) and v=tan^(-1)((2x)/(1-x^2)) , where -1

If u and v are the roots of the equation x^2+2x-2=0 , then the value of log_2(u^2+v^2)-log_2u^2-log_2v^2 is (a) -1 (b) 1 (c) 0 (d) -2

Let u = cot^(-1) sqrt(cos 2 theta) - tan^(-1) sqrt( cos 2 theta) , then the value of sin u is

int_(1)^(2)((x^(2)-1)dx)/(x^(3).sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where u and v are in their lowest form. Find the value of ((1000)u)/(v) .

If a ball strickes with a velocity u_(1) at the wall which itself is approaching it with a velocity u_(2) then find the velocity of the ball after collision with the wall.